Statistical Inference for a New Class of Multivariate Pareto Distributions

Abstract

Various solutions to the parameter estimation problem of a recently introduced multivariate Pareto distribution are developed and exemplified numerically. Namely, a density of the aforementioned multivariate Pareto distribution with respect to a dominating measure, rather than the corresponding Lebesgue measure, is specified and then employed to investigate the maximum likelihood estimation (MLE) approach. Also, in an attempt to fully enjoy the common shock origins of the multivariate model of interest, an adapted variant of the expectation-maximization (EM) algorithm is formulated and studied. The method of moments is discussed as a convenient way to obtain starting values for the numerical optimization procedures associated with the MLE and EM methods.

Keywords:

• Common shock model
• Expectation-maximization algorithm
• Maximum likelihood estimation
• Method of moments
• Multivariate Pareto distribution.

Mathematics Subject Classification:

• 62F10
• 62H12
• 60E05.